FRG: Collaborative Research: Mathematics of large scale urban crime

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This multidisciplinary project aims to develop new mathematical methods, at the interface of the theory of nonlinear partial differential equations, statistical mechanics, graph theory, and statistics, for predictability and control of urban crime. The project focuses on spatio-temporal crime patterns and includes (1) new mathematical analysis and comparisons to crime data for discrete and continuum models of crime hotspots; (2) models with spatially embedded social networks, especially with regard to gang activity; and (3) exploration of new methods of Geographic Profiling, incorporating detailed features of urban terrain and more accurate modes of criminal movement into existing models. Mathematical work on this project includes analysis of nonlinear PDE models, analysis of statistical physics models, and further development of these models to include spatial heterogeneity, different offender movement patterns, and urban street gang networks. At the same time it provides both a deeper understanding of the mechanisms behind pattern formation in urban crime and some useful algorithms and software for local law enforcement agencies.Mathematics of criminality is an emerging topic in applied mathematics with interest on a global scale and direct relevance to U.S. homeland security. This focused research group involves interactions between researchers whose primary expertise lies within very different fields -- mathematics, physics, anthropology, and criminology -- so that pattern formation of criminal activity is dissected and understood from very different viewpoints and perspectives. The project addresses algorithm development for analyzing real field data and agent-based simulation tools for urban crime. The research will also develop new models for urban crime and carry out mathematical analysis of these models. The project involves training of students and postdoctoral scholars at all levels, including a significant undergraduate component. Ph.D. students and postdoctoral scholars will also obtain valuable mentoring experience necessary for development of their research careers. The work includes direct interaction with local law enforcement agencies and the Institute for Pure and Applied Mathematics.